{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:BP5CKIYNCLWKMOIHSGLRIQG35R","short_pith_number":"pith:BP5CKIYN","canonical_record":{"source":{"id":"2605.20996","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T10:36:13Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"ef26d21e62999c15db3f882651c74de902cf830d45b8fe8cec4940ef3a5fce9e","abstract_canon_sha256":"21084af3584cd31e7f813b9e9044d4d25f059c0603d2d2e66c80cf88a7942446"},"schema_version":"1.0"},"canonical_sha256":"0bfa25230d12eca6390791971440dbec60872a1a577b76d2431d0283d1a57efb","source":{"kind":"arxiv","id":"2605.20996","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20996","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20996v1","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20996","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"BP5CKIYNCLWK","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"pith_short_16","alias_value":"BP5CKIYNCLWKMOIH","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"pith_short_8","alias_value":"BP5CKIYN","created_at":"2026-05-21T01:05:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:BP5CKIYNCLWKMOIHSGLRIQG35R","target":"record","payload":{"canonical_record":{"source":{"id":"2605.20996","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T10:36:13Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"ef26d21e62999c15db3f882651c74de902cf830d45b8fe8cec4940ef3a5fce9e","abstract_canon_sha256":"21084af3584cd31e7f813b9e9044d4d25f059c0603d2d2e66c80cf88a7942446"},"schema_version":"1.0"},"canonical_sha256":"0bfa25230d12eca6390791971440dbec60872a1a577b76d2431d0283d1a57efb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:31.633439Z","signature_b64":"KPFRZ4D+kczbW5w1UrZEg5/MiItk58qQgL5Qh6WraQbLIfnBrOi71Gstad7aeBYgzvG9er149wwBgImytas3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bfa25230d12eca6390791971440dbec60872a1a577b76d2431d0283d1a57efb","last_reissued_at":"2026-05-21T01:05:31.632680Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:31.632680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.20996","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4riOzN7oQGTx4ISuFRAG5b9n8roBKvLVwNkeXxifbrAds9zvjy9rMBbicRssiW14uzPeMHo923swCz2u58pwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:29:37.387848Z"},"content_sha256":"eb6d1efdbbcd7524cac537c508fabfccdb403b1ebaada1509c3a8c9f8600e007","schema_version":"1.0","event_id":"sha256:eb6d1efdbbcd7524cac537c508fabfccdb403b1ebaada1509c3a8c9f8600e007"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:BP5CKIYNCLWKMOIHSGLRIQG35R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beyond the Bellman Recursion: A Pontryagin-Guided Framework for Non-Exponential Discounting","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Hojin Ko, Jeonggyu Huh","submitted_at":"2026-05-20T10:36:13Z","abstract_excerpt":"Most value-based and actor--critic reinforcement learning methods rely on Bellman-style recursions, yet these recursions collapse under non-exponential discounting common in human preferences and survival processes. We show the breakdown is structural: exponential discounting sits at a fragile intersection of multiplicativity and time homogeneity, and violating either property breaks standard dynamic programming. To overcome this, we propose Pontryagin-Guided Direct Policy Optimization (PG-DPO), a variational framework that abandons recursion and couples the Pontryagin Maximum Principle with M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20996","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.20996/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJQCzHvllBeUPZv8uLB4IHXJ+eIKIKRlU9ZXPHsiZmR3KiH6X+9NJPTLTMk6maEQI0GL1Pc/EcZxeVYDKM7MAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:29:37.388235Z"},"content_sha256":"ce6fe4b7f659fb4689ca410480ced589db0918b5ed76891f8e265710efc5b3c1","schema_version":"1.0","event_id":"sha256:ce6fe4b7f659fb4689ca410480ced589db0918b5ed76891f8e265710efc5b3c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BP5CKIYNCLWKMOIHSGLRIQG35R/bundle.json","state_url":"https://pith.science/pith/BP5CKIYNCLWKMOIHSGLRIQG35R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BP5CKIYNCLWKMOIHSGLRIQG35R/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-22T19:29:37Z","links":{"resolver":"https://pith.science/pith/BP5CKIYNCLWKMOIHSGLRIQG35R","bundle":"https://pith.science/pith/BP5CKIYNCLWKMOIHSGLRIQG35R/bundle.json","state":"https://pith.science/pith/BP5CKIYNCLWKMOIHSGLRIQG35R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BP5CKIYNCLWKMOIHSGLRIQG35R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:BP5CKIYNCLWKMOIHSGLRIQG35R","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"21084af3584cd31e7f813b9e9044d4d25f059c0603d2d2e66c80cf88a7942446","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T10:36:13Z","title_canon_sha256":"ef26d21e62999c15db3f882651c74de902cf830d45b8fe8cec4940ef3a5fce9e"},"schema_version":"1.0","source":{"id":"2605.20996","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20996","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20996v1","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20996","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"BP5CKIYNCLWK","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"pith_short_16","alias_value":"BP5CKIYNCLWKMOIH","created_at":"2026-05-21T01:05:31Z"},{"alias_kind":"pith_short_8","alias_value":"BP5CKIYN","created_at":"2026-05-21T01:05:31Z"}],"graph_snapshots":[{"event_id":"sha256:ce6fe4b7f659fb4689ca410480ced589db0918b5ed76891f8e265710efc5b3c1","target":"graph","created_at":"2026-05-21T01:05:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.20996/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Most value-based and actor--critic reinforcement learning methods rely on Bellman-style recursions, yet these recursions collapse under non-exponential discounting common in human preferences and survival processes. We show the breakdown is structural: exponential discounting sits at a fragile intersection of multiplicativity and time homogeneity, and violating either property breaks standard dynamic programming. To overcome this, we propose Pontryagin-Guided Direct Policy Optimization (PG-DPO), a variational framework that abandons recursion and couples the Pontryagin Maximum Principle with M","authors_text":"Hojin Ko, Jeonggyu Huh","cross_cats":["math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T10:36:13Z","title":"Beyond the Bellman Recursion: A Pontryagin-Guided Framework for Non-Exponential Discounting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20996","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:eb6d1efdbbcd7524cac537c508fabfccdb403b1ebaada1509c3a8c9f8600e007","target":"record","created_at":"2026-05-21T01:05:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"21084af3584cd31e7f813b9e9044d4d25f059c0603d2d2e66c80cf88a7942446","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-20T10:36:13Z","title_canon_sha256":"ef26d21e62999c15db3f882651c74de902cf830d45b8fe8cec4940ef3a5fce9e"},"schema_version":"1.0","source":{"id":"2605.20996","kind":"arxiv","version":1}},"canonical_sha256":"0bfa25230d12eca6390791971440dbec60872a1a577b76d2431d0283d1a57efb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bfa25230d12eca6390791971440dbec60872a1a577b76d2431d0283d1a57efb","first_computed_at":"2026-05-21T01:05:31.632680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:31.632680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KPFRZ4D+kczbW5w1UrZEg5/MiItk58qQgL5Qh6WraQbLIfnBrOi71Gstad7aeBYgzvG9er149wwBgImytas3Cg==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:31.633439Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20996","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb6d1efdbbcd7524cac537c508fabfccdb403b1ebaada1509c3a8c9f8600e007","sha256:ce6fe4b7f659fb4689ca410480ced589db0918b5ed76891f8e265710efc5b3c1"],"state_sha256":"efa1e88127d2fccefed5f7a68714110d9a2f413175b5f73d0d392db5c5b44cf4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yJdMoTpfzk42hxJ8/EE8JYZ3iL7HYKAciy3q8GJIrXUQx3h5D+8Cz5MliuAJKLiSYDWm4hx+c+pRrYLsgkFVDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T19:29:37.390358Z","bundle_sha256":"c61c693ae271d1c4e7e00382615bd391472558acd281cb2772e5c634ad7dd171"}}